Stacked Chords

In Music, stacked chords are a set of well-defined pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain one interval.

5-limit tertiary harmonic triads

Name	Divides interval	Chord Formula	Odd Limit
Major Major	3/2	5/4 + 6/5 or M3 + m3	5
Minor	3/2	6/5 + 5/4 or m3 + M3	5
Augmented	25/16	5/4 + 5/4 or M3 + M3	25
Diminished Diminished	25/18	6/5 + 6/5 or m3 + m3	25

7-limit tertiary harmonic triads

Name	Divides interval	Chord Formula	Odd Limit
Septimal Major	3/2	9/7 + 7/6 or 7M3 + 7m3	9
Septimal Minor	3/2	7/6 + 9/7 or 7m3 + 7M3	9
Marvel-Tempered Augmented	14/9	5/4 + 5/4 or M3 + M3	9
Starling-Tempered Diminished	12/7	6/5 + 6/5 or m3 + m3	9

11-limit tertiary harmonic triads

Name	Divides interval	Chord Formula	Odd Limit
Neutral	3/2	11/9 + 11/9	11
7:9:11	11/7	9/7 + 11/9 or SM3 + N3	11